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Home » Solution: Total number of ways to choose 3 out of 8 stations: - Silent Sales Machine

Solution: Total number of ways to choose 3 out of 8 stations: - Silent Sales Machine

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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\cdot 9 \cdot 9 = 486
Now impose the even-sum condition.
Sum is even if number of odd addends is even (since even + even = even...
Prime numbers: 2 (even), 3, 5 (odd) → primes: one even (2), two odd
Non-primes: 1 (odd), 4, 6 (even) → non-primes: one odd (1), two even (...
We need the total sum to be even, with exactly two prime rolls and two...
$ p \in \{2, 3, 5\} $: contributes parity: even if 2, odd otherwise
$ np \in \{1, 4, 6\} $: contributes: odd (1), even (4,6)
Let $ E $ = total number of odd numbers among the four rolls. We want...
2 primes: one even (2), two odd (3,5)

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Correct model: The volumes are:
\(V_1 = 729\)
\(V_2 = 729 \times 1/2 = 364.5\)
But 364.5 < 729, so only one bottle fits.
But question implies multiple.
Insight: Perhaps "each holds half of the previous" starts after the fi...
Another possibility: The initial 729 ml is split into portions where e...
But without constraint on total capacity, infinite.
Final realization: This is a geometric series where total volume is 72...
But question says "fill the entire solution" — total volume is 729.

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